Central Limit Results for Jump-Diffusions with Mean Field Interaction and a Common Factor

2014/05/29 by Budhiraja, A., Kira, E., Saha, Subhamay
#60F05 #60H30 #60J70 #60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1405.7682

Abstract

A system of N weakly interacting particles whose dynamics is given in terms of jump-diffusions with a common factor is considered. The common factor is described through another jump-diffusion and the coefficients of the evolution equation for each particle depend, in addition to its own state value, on the empirical measure of the states of the N particles and the common factor. A Central Limit Theorem, as N → ∞, is established. The limit law is described in terms of a certain Gaussian mixture. An application to models in Mathematical Finance of self-excited correlated defaults is described.

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